Celestial
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Equation Of TIME
By
Capt. Abdelhamid Elkady
Relation Between Greenwich
and Local Time
GMT
West East
Greenwich
England Sun gets here before GMT
Sun gets here after GMT so times here are earlier than GMT
so times here are later than GMT
Relation Between Greenwich
and Local Time
LONG W LONG E
SOLVED EXAMPLE (1)
If L.M.T. 15h 13m 39s Apr. 19th was recorded for an observer in Long. 123° 22' W.
Calculate L.M.T. at the same moment for an observer in Long. 123° 22' E.
L.M.T 15h 13m 39s Apr. 19th
L.1/T 08h 13m 28s
w+
G.M.T 23h 27m 07s Apr. 19th
L2./T 08h 13m 28s
E+ 07h 40m 35s Apr. 20th
L.M.T
SOLVED EXAMPLE (1)
If L.M.T. 02h 40m 18s May 7th was recorded for an observer in Long. 68° 51'.3 E.
Calculate L.M.T. at the same moment for an observer in Long. 98° 48'.5 W.
24h
L.M.T 02h 40m 18s May r7th
L1./T 04h 35m 25s
E-
G.M.T 22h 04m 53s May 6th
L2./T 06h 35m 14s
W- 15h 29m 39s May 6th
L.M.T
Equation NCPOf TIME
L.H.A Ts L.H.A ms
± 12 H ± 12 H
L.A.T ~ L.M.T =
Eclipti
c
Equation of
Time Q’ Q
L.H.A
MS
L.H.A
TS
SCP
Equation Of TIME
"The Equation of time is the
difference between apparent
time(A.T) and mean time
(M.T) or numerically equal to
the difference between the
hour angles of apparent and
mean suns"
It is positive (+) if the meridian of the
true sun in diurnal motion is a head
of the meridian of the mean sun, and
negative (-) if behind
Cases of applying Eq. of
. Time
Case (1) : ( if eq. of. T is given )
The eq.of. T is to be applied to the
( M.T ) with its sign
If applied to the ( A.T ) the sign should
be reversed
M.T A.T
Eq.of .T (as it is) Eq.of .T ( reverse
A.T sign )
M.T
EXAMPLE (2) : ( if eq. of. T is given )
IF LMT= 03h 20m 10s and equation of
time= +10m 20s
Calculate the LAT?
LM.T = 03h 20m
10s
Eq.of .T= + 10m
20s
LAT = 03h 30m
30s
EXAMPLE (3) : ( if eq. of. T is given )
IF LAT= 14h 50m 40s and equation of
time= +10m 20s
Calculate the LMT?
LAT = 14h 50m
40s
Eq.of .T= - 10m
20s
LM.T = 14h 40m
20s
Case (3) : If Eq.of.T is needed to
convert type of Time to another
AT NOON TIME ( UPPER MERIDIAN PASSAGE )
THE SUN CROSSES THE UPPER MERIDIAN OF
THE OBSERVER ANY WHERE
THE L.A.T AT THIS MOMENT IS ( L.A.T MP =
12 00 00 )
G.A.T
L.A.T G.M.T
L.M.T
Eq.of. T
Eq.of. T ±
A.T < M.T eq.of. Time
negative
eq.of. Time = 12 00 00 _
EXAMPLE (4) : Sun crossed the upper
observer’s meridian at LMT= 12h 04m
30s Calculate the equation of time?
L.A.T MP = 12
00 00
LM.T = 12h
04m 30s
Eq.of .T= - 04m
30s
EXAMPLE (5) : Sun crossed the upper
observer’s meridian at LMT= 11h 58m
10s Calculate the equation of time?
L.A.T MP = 12 00
00
LM.T = 11h 58m
10s
Eq.of .T = +
01m 50s
Case (3) If eq.of.T is needed to
convert type of Time to another
Example 6:
If LMT was recorded 20h 30m 10s
19th July, 1990, for an observer in Longitude 74° 45’ w
Calculate the GAT at the same moment.
LMT =20h 30m 10s 19th July
L/t w +=04h 59m 00s
GMT = 01h 29m 10s 20th
July
Eq.T =- 00h 06m 18s
GAT = 01h 22m 57s 20th July
Mer. Pass 12h 06m
> 12 00
LMT > LAT
Eq.of T.
LMT LAT
Long./T E – ,W+ Long./T E + ,W-
GMT Eq.of T. GAT
Example 6:
If LAT was recorded 10h 50m 40s 10 th Jan.,
1990, for an observer in Longitude 100° 30’ E
Calculate the GMT at the same moment.
LAT =10h 50m 40s 10th
Jan
L/t E -=06h 42m 00s
GAT = 04h 08m 40s 10th
Jan
Eq.T =+ 00h 12 07m 22s
12 12
GMT = 04h 16mh 02s 20th Jan
h s 00h 12h
07m 18s 07m 30s
04h 08m X
Mer. Pass 12h 07m
X=4s 12 > 12 00
s MT > AT
Eq.ofT=4s+7m 18s= 7m 22s
Example 7:
If LAT 7h 41m 33s April 20 was recorded for an
observer in Long. 123° 22'.0 E. Calculate LM.T. at the
same moment for an observer in Long. 123°22'.0 W.
LAT = 7h 41m 33s April 20
L1/t E - =08h 13m 28s
GAT 1200= 23h 28m 05s 19th Apil
Eq.T =- 00h 00m 58s
GMT11m58s = 23h 27m 07s 19th Apil
L2/t w - =08h 13m 28s
LMT = 15h 13m 39s 19th Apil
Mer. Pass 11h 59m
< 12 00
23h 28m 05s near to 00h on 20th April MT < AT
So we can take the Eq.T 00m
58s
Example 8:Calculate the length of apparent
solar day of March 2nd
Eq. of . Time (00h) Mar. 2nd 12
Eq. of . Time (00h) Mar. 3rd 18
12
Diff. of eq. 06
Mean Day 1212 12 s
Diff. of eq. -
App. Solar day 1200
24h 00m
00s 12 s
Mer. Pass 12h 12m
23h 59m > 12 00
48s MT > AT
Example 9 Calculate the length of apparent
solar day of Sept. 26th
Eq. of . Time (00h) Sept. 26th 08
Eq. of . Time (00h) Sept. 27thr 25
08
Diff. of eq 45 20 s
Mean Day 1151
+
App. Solar day 1200
24h 00m
00s 20 s
Mer. Pass 11h 51m
< 12 00
24h 00m MT < AT
20s
Long Eq. of. T 12 H
Changes the first Changes the middle Changes the last 2
letter letter letter
L → M → A H.A
G A → M → ..T
G → L ..T →
L.M.T L.M.T H.A
L.H.A ms
Long/T Eq .of . T ± 12 H
G.M.T L.A.T L.M.T
G.H.A G. A . T G. A . T
Long Eq .of . T ± 12 H
L.H.A G .M .T G .H.A Ts
If LMT 07h 20m 33s May 23rd for an observer
in long 96 34 E
Find the GMT
LMT 07 20 33
May 23
Long / T E
GMT — 06 26 16
00 54 17
May 23
Long E G least
Long W G Best
If LMT 21h 30m 53s June 27th for an
observer in long 126 34 w
Find the GMT
LMT 21 30 53
June 27
Long / T w
GMT + 8 26 16
29
05 57 09 June
28
27
Long E G lest
Long W G Best
If GMT 03h 20m 50s May 17th
Find the LMT for an observer in long 137
30 E
GMT 03 20 50
May 17
Long / T E
LMT + 9 10 00
12 30 50
May 17
Long E G least
Long W G Best
